Business Mathematics and Statistics

St. Joseph’s College of Commerce BBM 2013 I Sem Business Mathematics And Statistics Question Paper PDF Download

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1
ST. JOSEPH’S COLLEGE OF COMMERCE (AUTONOMOUS)
END SEMESTER EXAMINATION – OCTOBER 2013
BBM – I SEMESTER
BUSINESS MATHEMATICS AND STATISTICS
Time : 3 HOURS Max. Marks : 100
SECTION – A
I) Answer ALL the questions. (10x 2 = 20)
1) Solve: (2x-7)(3x+1)=(2x-5)(3x-1).
2) Find the Simple interest on Rs. 17,000 for 3 months at 4% P.a.
3) Define Statistics.
4) Mention any 4 applications of statistics.
5) Arun can do a piece of work in 8 days, which Bala alone can do in 10 days. In
how many days both working together can do it?
6) Ramesh, Mohan and Chandra start a business jointly. Twice the investment of
Ramesh is equal to thrice the capital of Mohan and the capital of Mohan is four
times the capital of Chandra. Find the share of Mohan in an annual profit of
2,97,000.
7) A reduction of 20% in the price of sugar enables a man to purchase 4 kg more of
Rs. 280. What is the original rate and what is the reduced rate?
8) Solve x2-6x-72=0.
9) A company needs Rs. 10,00,000 at the end of 5 years from now. It would like to
set aside equal amount each year out of its profits. If the present market rate of
interest is 16%. How much of annual amount should be invested?
10) How is the value of r in Karl Pearson’s coefficient of correlation interpreted?
SECTION – B
II) Answer ANY FOUR of the following. (4×5=20)
11) Describe the characteristics of statistics.
12) Explain the limitations and scope of Statistics.
13) The following are heights in centimetres of 40 students. Form the frequency
distribution with appropriate class interval. 163.3, 155.0, 163.9, 163.9, 148.2, 151.5,
178.9, 155, 146.1, 145.2, 156.6, 159.9, 158.0, 153.4, 160.0, 149.3, 154.2, 164.7, 159.0,
160.8, 157.1, 176, 164.4, 170.0, 152.9, 169.3, 159.5, 162.4, 173.6, 154.8, 158.3, 172.5,
158.0, 154.0, 172.2, 148.0, 152.4, 156.6, 157.7, 165.3
2
14) Locate the Median and Quartiles from the following data.
Size of
shoes
Frequencie
s
4 20
4.5 36
5 44
5.5 50
6 80
6.5 30
7 30
7.5 16
8 14
15)A sum of Rs.8448 is divided between 2 persons A and B who are respectively 18 years
and 19 years old in such a way that their shares be invested at 6.25% per annum
compound interest. They shall receive equal amount on attaining the age of 21 years.
How should the sum be divided. How much will each receive when 21 years old?
16)Draw a histogram from the following and locate the mode. verify it by actual
calculations.
Class
Interval
Frequencies
0-10 14
10-20 23
20-30 35
30-40 20
40-50 8
50-60 5
SECTION -C
III) Answer ANY THREE of the following questions. (3×15=45)
17) a) Explain the functions of Statistics?
b) Describe the uses of Statistics?
18) a) Following are the runs scored by 2 batsmen in 10 innings. Find who is a
better scorer and who is more consistent.
Player1-101, 22, 0, 36, 82, 45,7,13, 65, 14
Player2- 97, 12, 40, 96, 13,8, 85 ,8, 56,16.
3
b) Draw Ogives from the following data and measure the median value. verify it by
actual calculations.
Mid point: 5 15 25 35 45.
Frequency: 5 11 21 16 10.
19) The life of 2 types of tyres in a sample survey is given below.
Life
(kms)
Number of
Tyres of Type
A
Number of
Tyres of
Type B
5000-10000 10 18
10000-15000 18 22
15000-20000 32 40
20000-25000 40 32
25000-30000 22 18
30000-35000 18 10
a) Which of the 2 makes has a higher average life?
b) If prices are same for both the types, which type would you prefer and why?
20) The competitors of a beauty contest were ranked by 3 judges as follows:
Judge A: 3 5 4 10 8 8 1 6 8 2
Judge B: 5.5 5.5 1 8.5 4 10 2 7 8.5 3
Judge c: 9 9 7 5 2 2 2 5 5 9
21) a) The following data relates to the ages of husbands and wives.
Age of the
Husband : 25 28 30 32 35 36 38 39 42 55
Age of wife: 20 26 29 30 25 18 26 35 35 46.
Obtain the two regression equations and determine the most likely age of
husband for the age of wife of 25 years.
b) Define and explain the different types of Annuity.
22) a) Compute the mean runs scored by a batsman from the following data.
Runs Scored: 10 20 30 40 50 60 70 80 90
Number of : 7 8 15 25 30 20 16 7 2.
Batsmen
4
b) Represent the following data in a suitable diagram
Newspaper Daily
Sales
Times of India 1432000
Deccan Herald 1431000
Indian Express 1327000
Asian Age 1119000
Hindustan times 894000
6.3) if the mean of a set of scores is 20, median is 22.Find the mode?
SECTION – D
IV) Compulsory question. (15 marks)
23) a) Compute the Karl Pearson’s coefficient of correlation between per capita
national income and per capita consumer expenditure from the data given
below. (8 marks)
Year
Per
capita
National
Income
Per capita
consumer
expenditure
1978 249 237
1979 251 238
1980 248 236
1981 252 240
1982 258 245
1983 269 255
1984 271 254
1985 272 252
1986 280 258
1987 275 251
b) LIC offers a special annuity scheme called the Jeevan Dhara scheme. One of
the options in this scheme is as follows. If a lump sum amount is paid now,
the LIC will pay an annuity of Rs.12000 commencing from the end of 1st year
till the person’s death. Assuming that LIC allows 9% P.a rate of interest and
the person’s life expectation is 15 years, how much should be deposited in
lump sum now. (7 marks)
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St. Joseph’s College of Commerce B.B.M. 2014 I Sem Business Mathematics And Statistics Question Paper PDF Download

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  1. JOSEPH’S COLLEGE OF COMMERCE (AUTONOMOUS)

END SEMESTER EXAMINATION – OCTOBER 2014

B.B.M. – I SEMESTER

 BUSINESS MATHEMATICS AND STATISTICS

Duration: 3 Hours                                                                                           Max. Marks: 100

SECTION – A

  1. Answer ALL the questions. Each carries 2 marks.                                       (10 x2 =20)

 

  1. Statistics has been referred to as the science of universal applicability, explain.
  2. What are positional averages? Give a brief description of two such averages.
  3. 20 men can do a job in 90 days. How many days are needed for 30 men to do the same job?
  4. What are the essentials of a good graph?
  5. Monthly incomes of A and B are in the ratio of 4 : 5 and their monthly expenses are in the ratio of 7 : 9. Their savings are in the ratio 4 : 3.  If the total savings are Rs. 350, find their monthly incomes.
  6. Distinguish between Mean Deviation and Standard Deviation.
  7. The cash price of a machine is Rs. 11,400. The trade discount and cash discount are 20% and 5% respectively.  Find its List Price.
  8. Define correlation. Give its significance.
  9. In an examination 70% of the candidates passed in English, 65% in Mathematics, 27% failed in both subjects and 248 passed in both subjects. Find the total number of candidates.
  10. The mean age of 40 students is 16 years and the age of other 60 students is 20 years. Find the mean age of all the 100 students taken together.

 

SECTION – B

 

  1. Answer any FOUR Each carries 5 marks.                                 (4×5=20)

 

  1. Present the following information in a suitable tabular form:

In 2005 out of total 2000 workers in a factory, 1550 were members of a trade union.  The number of women workers employed was 250, out of which 200 did not belong to any trade union.  In 2010, the number of union workers was 1725 of which 1600 were men.  The number of non-union workers was 380, among which 155 were women.

 

 

  1. Calculate mode from the following data:
X: 0-5 5-10 10-20 20-30 30-40 40-50 50-60 60-70
f: 128 150 520 464 398 324 178 44

 

  1. Solve by factors: 6x2 – x – 35 = 0
  2. Find the principal for which the difference of simple interest and compound interest for 2 years is Rs. 20 at 4% p.a.

 

  1. Solve: 3/(x2 – 4) + 2/(x + 2) = 1/(x – 2).

 

  1. A family spends the following percentage of expenditure on different commodities, prepare circular diagram for these expenditures:

Items of Expenditure                                   % to Total

Food                                                               60

Clothing                                                         12

Housing                                                         10

Fuel and Lighting                                          8

Others                                                                        10

Total                                                             100

 

  1. Eight students have obtained the following marks in Hindi and Economics. Calculate the Rank Co-efficient of Correlation.
Hindi 25 30 38 22 50 70 30 90
Economics 50 40 60 40 30 20 40 70

 

 

SECTION – C

 

III)      Answer any THREE questions.    Each carries 15 marks.                    (3×15=45)

 

  1. Discuss the characteristics and limitations of Statistics.
  2. Mr. Shan desires to set up an endowment fund to provide for a prize of Rs. 500 every year. If the fund can be invested at 8% p.a. compound interest, find the amount of endowment.            (12+3)

 

  1. A company intends to create a fund to replace, at the end of the 25th year, asset costing Rs. 1,00,000. Calculate the amount to be retained out of profits every year, if interest rate is 3%.

 

 

  1. Calculate the Quartile Deviation and its Coefficient from the following data:
Marks 0-10 10-20 20-30 30-40 40-50
No. of Students 4 15 28 16 7

(5+10)

 

  1. The following table gives the soil temperature and the germination time at various places.
Temperature 45 70 65 30 90 40 50 75 85 60
Germination 35 90 70 40 95 40 60 80 80 50

Calculate Karl Pearson’s Coefficient of Correlation and interpret the value.  Also determine if the value of r is significant or not?

 

  1. The perimeter of a rectangular carpet is 38 meters and its area is 84 sq. cm. Find its dimensions.

 

  1. Calculate Standard Deviation from the following data:
Marks 12 14 16 18 20 22 24
No. of Students 6 12 18 26 16 10 8

(5+10)

  1. Given a bivariate data:
X 2 6 4 3 2 2 8 5
Y 7 2 1 1 2 3 2 6
  1. Fit the regression line of Y on X and hence predict Y, if X = 20
  2. Fit the regression line of X on Y and hence predict X, if Y = 5.

 

SECTION – D

 

  1. IV) Case study- Compulsory questions. (15 marks)
  2. There are two numbers such that the sum of the first and three times the second is 53, while the difference between 4 times the first and twice the second is 2. Find the numbers.

 

  1. Find the missing frequency when median is given to be 28:
X 0-10 10-20 20-30 30-40 40-50
f 5 8 ? 16 6

 

Also represent Median in a graph using only the Less Than Ogive.

                                                                                                             (5+10)

 

St. Joseph’s College of Commerce 2015 Business Mathematics And Statistics Question Paper PDF Download

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ST. JOSEPH’S COLLEGE OF COMMERCE (AUTONOMOUS)
END SEMESTER EXAMINATION – SEPT/OCT. 2015
B.B.A. – I SEMESTER
M1 15AR104: BUSINESS MATHEMATICS AND STATISTICS
Duration: 3 Hours                                                                                             Max. Marks: 100
SECTION – A
I) Answer ALL the questions.  Each carries 2 marks.                                        (10×2=20)
  1. Statistics can be understood in two senses.  Explain both with an example.
  2. Mention the laws of division and negative indices along with an example.
  3. State if the following are true or false:

i.                    (1000)0 = 0

ii.                 (4x)2     = 4x2

iii.               x4 + x2 = x6

iv.               (9/7)5  = 95/75
  4. Explain four criterions on which data can be classified.
  5. What is an Annuity?  Explain Annuity Due and Deferred Annuity.
  6. Solve: (5/2)x + 7/3 = (5/3)x – (1/3)
  7. A man sold an article for Rs. 161, gaining 1/6th of his outlay.  Find the cost price of the article.
  8. What is coefficient of dispersion?  What purpose does it serve?
  9. Find the coefficient of variation (standard deviation), if the sum of squares of the deviation of 10 observations taken from the mean 50 is 250.
  10. If A:B = 3:4, B:C = 5:9 and C:D = 16:15, find the ratio between A and D.
SECTION – B
II) Answer any FOUR questions.  Each carries 5 marks.                                      (4×5=20)
  11. i. A firm wishes to forecast sales data for the month of July on the basis of weighted average of the past data of four months.  It assigns 0.10, 0.25, 0.25 and 0.4 weights to the actual sales data of past four months.  Monthly sales for the months of March, April, May and June of a firm was found to be 350, 450, 400, 600 units.  Forecast sales data for the month of July by using weighted average.

 

ii. Two quantities are in the ratio 3:4 and if 10 is subtracted from each of them, the remainders are in the ratio 1:3.  What are the quantities?
  12. A stock broker firm has its head office in Mumbai and branch office in Delhi.  For the year 2010, it supplied the following information:

Mumbai              Delhi

Number of transactions done                                    5470                    1130

Average profit per transaction (Rs.)                           300                      200

From the above information calculate the average profit for the stock brokers per transaction by taking both the offices together.
  13. Municipal Corporation of Delhi collected the following amount of tax form roaming traders in a busy market:

Amount of Tax (Rs.):     25         50           75          100           200         300

No. of Traders:              135       120          90            60            55            40

From the above data of tax collections, calculate Q.D. and coefficient of Q.D.
  14. i. The average monthly income from interest for a housewife is Rs. 810 and the related median is Rs. 795.  Calculate modal interest income.

ii. Find the amount in case the principal is Rs. 10,000 and the rate of compound interest is 5% p.a. for 2 yrs. if the compound interest is paid quarterly.
  15. “Positive correlation is found between the number of children born and exports over the last decade”, comment.  Also explain the different types of correlation with examples.
  16. Ashok lent two equal sum of money to Rahul and Laxman.  While Rahul agreed to pay interest @ 5% p.a., simple interest, Laxman will pay interest @ 6% p.a., simple interest.  At the end of 10 yrs. Ashok received Rs. 1,000 more from Laxman towards interest.  How much did Ashok lend to Rahul and Laxman each?
SECTION – C
III) Answer any THREE questions.  Each carries 15 marks.                                (3×15=45)                                                                                                 
  17. The following table shows the number of motor registrations in a certain territory for a term of 5 yrs. and the sale of motor tyres by a firm in the territory for the same period.

Year Motor registration No. of tyres sold
1

2

3

4

5

 600

630

720

750

800

 1,250

1,100

1,300

1,350

1,500

Find the regression equation to estimate the sale of tyres when the motor registration is known.  Estimate sale of tyres when registration is 850.
  18. i. X,Y & Z start a business jointly.  Twice the investment of X is equal to thrice the capital of Y and the capital of Y is four times the capital of Z.  Find the share of X,Y & Z in an annual profit of Rs. 2,50,000.                                       (5m)

ii. A survey was conducted in a city hospital and the amount spent by 150 patients is given in the following table.  The median expenditure was found to be Rs. 909.52.  Calculate the two missing frequencies.                                   (10m)

Amount (Rs.) Number of Patients
200-400 8
400-600 14
600-800 ?
800-1000 42
1000-1200 27
1200-1400 ?
1400-1600 10
   

 

19.

  

 

Share prices of two companies A Ltd. and B Ltd. are recorded as follows:

A Ltd.:     12        13        15        14        14        14        13        17

B Ltd.:     113      114      113      115      117      114      112      114

Which company’s share prices are more variable?
  20. Following is the playing habit of certain students.  Find Karl Pearson’s correlation.  Also calculate probable error and point out whether ‘r’ is significant.

Age (years):                                              15        16        17        18        19        20

Percentage of no. of regular players:    80        75        60        40        30        15
  21. i. A and B can complete a piece of work in 12 days, A and C in 15 days, B and C in 18 days.  They work together for 5 days when A leaves.  B and C continue the work for 7 days more, when B leaves.  How long should it take for C to finish it?                                                                                                                  (8m)

 

ii. There are two numbers such that the sum of the first and three times the second is 53, while the difference between 4 times the first and twice the second is 2.  Find the numbers.                                                                           (7m)
SECTION – D
IV) Case Study                                                                                                              (1×15=15)                                                                                           
  22. i. Following table shows the distance travelled in kilometers by executives of an IT company:

Distance travelled (in ‘000s kms.) No. of executives
0-10 35
10-20 50
20-30 65
30-40 80
40-50 72
50-60 24
60-70 18

 

Calculate mode from the above figures by graphic method.                         (7m)

 

ii. A father wants to send his child for higher studies after 15 yrs.  He expects the cost of higher studies then to be Rs. 1,00,000.  How much should he save annually to have Rs. 1,00,000 after 15 years if the interest rate is 12% p.a.? (4m)

 

iii. A person bought an article and sold it at a profit of 20% on his purchase cost.  Had he bought at 20% less, what would have been the profit percentage, if the selling price had been the same?                                                              (4m)

 

 

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